Question

How many structural and geometrical isomers are possible for dimethyl cyclohexane? (a) 3,3 (b) 3,6 (c) 6,6 (d) 6,3

Short answer

Option (b) 3,6.

Step-by-step solution

Understanding the Problem

Dimethyl cyclohexane is a compound formed by substituting two hydrogen atoms in cyclohexane with methyl groups. The goal is to identify the number of possible structural (constitutional) isomers and the number of geometrical (cis-trans) isomers.

Finding Structural Isomers

Structural isomers are compounds with the same molecular formula but different structural arrangements. For dimethyl cyclohexane, we place the two methyl groups on the cyclohexane ring in different positions: 1. 1,1-dimethylcyclohexane: Both methyl groups on the same carbon. 2. 1,2-dimethylcyclohexane: Methyl groups on adjacent carbons (ortho position). 3. 1,3-dimethylcyclohexane: Methyl groups with one carbon in between (meta position). 4. 1,4-dimethylcyclohexane: Methyl groups on opposite carbons (para position). Thus, there are 4 structural isomers.

Determining Geometrical Isomers

Geometrical isomers have the same structural formula but differ in the orientation of groups around a double bond or a ring. For 1,2-, 1,3-, and 1,4-dimethylcyclohexane, cis and trans forms are possible since the ring restricts rotation: 1. 1,2-dimethylcyclohexane: Possible as cis (both methyls on the same side) and trans (methyls on opposite sides). 2. 1,3-dimethylcyclohexane: Also has cis and trans forms. 3. 1,4-dimethylcyclohexane: Has cis and trans forms. Thus, for these 3 structural isomers (excluding 1,1-dimethyl which doesn't have geometrical forms), there are a total of 2 (cis and trans) x 3 = 6 geometrical isomers.

Summarizing and Matching Choices

Summarize the count: 4 structural isomers and 6 geometrical isomers. Look for an option matching this count. The option that matches is (b) 3,6 because it refers to 3 structural isomers having geometrical isomers (the 1,2; 1,3; and 1,4 arrangements) and 6 geometrical (cis-trans) isomers from the above combinations.

Key concepts

Structural Isomers

In organic chemistry, structural isomers are fascinating because they share the same molecular formula but differ in the connectivity of their atoms. This creates distinct molecules with varying properties and characteristics.

• Each isomer has the same kinds of atoms but arranged differently, offering diverse chemical properties.
• For dimethyl cyclohexane, we consider how the two methyl groups can be positioned on the cyclohexane ring.

Let's imagine the methyl groups hopping around the cyclic ring of cyclohexane. They can settle in the following ways:

• **1,1-dimethylcyclohexane**: Both methyl groups snugly fit onto the same carbon atom.


• **1,2-dimethylcyclohexane**: The methyl groups sit next to each other on adjacent carbon atoms.


• **1,3-dimethylcyclohexane**: Here, a carbon atom separates the two methyl groups, spaced at a meta position.


• **1,4-dimethylcyclohexane**: Positioned directly opposite each other; it’s like they’re playing on opposite teams across the ring.

With four distinct arrangements for dimethyl cyclohexane, we identify four structural isomers.

Geometrical Isomers

Geometrical isomers shine in compounds like dimethyl cyclohexane, where the inflexible structure prevents rotation around the bonded atoms. This uniqueness arises from the fixed angles between atoms in rings and double bonds.

• Unlike structural isomers, geometrical isomers have the same connectivity of atoms but differ in spatial arrangement.
• Their presence becomes notable when analyzing cycles and alkenes where rotations are hindered.

For dimethyl cyclohexane, the lack of rotation means we can have different 3D arrangements:

• **1,2-dimethylcyclohexane**: Imagine sitting the methyl groups on the same side of the plane (cis) or opposite sides (trans).


• **1,3-dimethylcyclohexane**: Similarly, the two methyl groups can appear on the same side (cis) or opposite (trans).


• **1,4-dimethylcyclohexane**: Methyl groups remaining in cis or trans positions relative to the plane.

This creates a scenario where we find intriguing variations in properties, thanks to these six geometrical arrangements.

Dimethyl Cyclohexane

Dimethyl cyclohexane is an example of a substituted cyclohexane, where two hydrogen atoms are replaced with methyl groups. This simple modification introduces a realm of isomerism, showcasing organic chemistry's complexity.

• Cyclohexane, a basic cyclic alkane, forms the backbone for this compound.
• The introduction of two methyl groups leads to an array of structural and geometrical isomers.

Visualize cyclohexane as a playground where the methyl groups can situate themselves in various playground zones, leading to four different structural isomers, as explained earlier.
In dimethyl cyclohexane, the two methyl groups must share space harmoniously in the cyclic structure, each settling into positions that allow for different structural arrangements and spatial orientations. This results in a dynamic assortment of isomers that are chemically similar yet distinct.

Cis-Trans Isomerism

Cis-trans isomerism, a subclass of stereoisomerism, takes the spotlight when looking into isomers of compounds like dimethyl cyclohexane. It’s all about the direction or orientation of substituents relative to a reference plane.

• In the cis form, substituents reside on the same side, offering a cozier arrangement.
• Meanwhile, in the trans form, they oppose each other across the plane.

This isomerism is visible in cyclic compounds and double-bonded molecules where flexibility is constrained.
For instance, in dimensional cyclohexane:

• You find **cis-1,2-dimethylcyclohexane** where the methyl groups stay buddy-buddy on the same face of the ring.
• In **trans-1,2-dimethylcyclohexane**, they’re more like competitors on opposite sides of the ring.

Such isomerism leads to distinctions in chemical and physical properties, which helps us understand and utilize each isomer's unique characteristics in practical applications.